Comment on "Mass and Width of the Lowest Resonance in QCD"

TL;DR

This paper critically examines and challenges the theoretical methods and error estimates used in previous analyses of the sigma and kappa meson resonances in QCD, highlighting significant flaws and uncertainties.

Contribution

It provides a theoretical critique of prior formalism and error analysis in the determination of meson resonance properties in QCD.

Findings

Identifies flaws in the theoretical formalism used by CCL.

Argues the error bars on sigma-meson mass and width are underestimated.

Highlights similar issues in the analysis of kappa-meson mass.

Abstract

I. Caprini's, G. Colangelo's, and H. Leutwyler's (CCL) article "Mass and Width of the Lowest Resonance in QCD", Phys. Rev. Lett. 96, 132001 (2006) [hep-ph/0512364], is critically reviewed. The present comment is devoted to complement a recent experimental discussion (D.V. Bugg, J. Phys. G 34, 151 (2007) [hep-ph/0608081]) of short-comings in the CCL analysis, by presenting theoretical arguments pointing at a serious flaw in the theoretical formalism used by CCL, and also at the unlikeliness of their tiny error bars in the sigma-meson mass and width. The criticism made in the comment applies analogously to the analysis on the kappa-meson mass performed in the article "The K0*(800) scalar resonance from Roy-Steiner representations of pi K scattering" published as S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C 48, 553 (2006) [hep-ph/0607133].